Sequence of current pulses for depinning magnetic domain walls

ABSTRACT

A method and structure for depinning a domain wall that is in spatial confinement by a pinning potential to within a local region of a magnetic device. At least one current pulse applied to the domain has a pulse length sufficiently close to a precession period of the domain wall motion and the current pulses are separated by a pulse interval sufficiently close to the precession period such that: the at least one current pulse causes a depinning of the domain wall such that the domain wall escapes the spatial confinement; and each current pulse has an amplitude less than the minimum amplitude of a direct current that would cause the depinning if the direct current were applied to the domain wall instead of the at least one current pulse. The pulse length and pulse interval may be in a range of 25% to 75% of the precession period.

This application is a continuation application claiming priority to Ser.No. 11/622,644, filed Jan. 12, 2007.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with government support under CooperativeAgreement No. H94003-05-2-0505 awarded by the U.S. Department ofDefense. The government has certain rights in the invention.

CROSS REFERENCE TO RELATED APPLICATIONS

This patent application is related to co-pending U.S. patent applicationSer. No. 11/004,413, filed Dec. 4, 2004, titled “System and Method ForTransferring Data To and From a Magnetic Shift Register With a ShiftableData Column”, which is related to U.S. patent application Ser. No.10/458,554, filed Jun. 10, 2003, titled “Shiftable Magnetic ShiftRegister and Method of Using the Same”, now issued as U.S. Pat. No.6,834,005.

FIELD OF THE INVENTION

The present invention relates to moving magnetic domain walls by currentpulses.

BACKGROUND OF THE INVENTION

Semiconductor magnetoresistive random access memory (MRAM) stores dataas direction of magnetic moment in a ferromagnetic material. Atoms inferromagnetic materials respond to external magnetic fields, aligningtheir magnetic moments to the direction of the applied magnetic field.When the field is removed, the magnetic moments still remain aligned inthe induced direction. A field applied in the opposite direction cancause the magnetic moments to realign themselves with the new directionif the field is large enough. Typically, the magnetic moments of theatoms within a volume of the ferromagnetic material are aligned parallelto one another by a magnetic exchange interaction. These magneticmoments then respond together, largely as one macro-magnetic moment, ormagnetic domain, to the external magnetic field

A domain wall between magnetic domains may be spatially confined by apotential well such that a substantial amount of applied energy isrequired to move the domain wall away from the potential well to nolonger be spatially confined by the potential well. Thus there is a needto provide a method and structure for moving the domain wall away fromthe potential well to no longer be spatially confined by the potentialwell, by using less applied energy than is presently used in the relatedart.

SUMMARY OF THE INVENTION

The present invention provides a method for depinning a domain wall,comprising applying at least one current pulse to a domain wall that isin spatial confinement by a pinning potential to within a local regionof a magnetic device, wherein each current pulse has a pulse lengthsufficiently close to a precession period of the domain wall motion andif the at least one current pulse comprises at least two current pulsesthen the current pulses are separated from each other by a pulseinterval sufficiently close to the precession period such that:

the at least one current pulse is configured to cause a depinning of thedomain wall such that the domain wall moves with sufficient energy toescape the spatial confinement; and

each current pulse has an amplitude less than the minimum amplitude of adirect current that would cause said depinning if the direct currentwere applied to the domain wall instead of the at least one currentpulse.

The present invention provides a method for depinning a domain wall,comprising:

applying at least one current pulse to a domain wall that is in spatialconfinement by a pinning potential to within a local region of amagnetic device,

wherein each current pulse has a pulse length in a range of 25% to 75%of a precession period of the domain wall motion and if the at least onecurrent pulse comprises at least two current pulses then the currentpulses are separated from each other by a pulse interval in the range of25% to 75% of the precession period, and

wherein the applied at least one current pulse is configured to cause adepinning of the domain wall such that the domain wall moves withsufficient energy to escape the spatial confinement.

The present invention provides a structure, comprising a domain wallthat is in spatial confinement by a pinning potential to within a localregion of a magnetic device and at least one current pulse applied tothe domain wall, wherein each current pulse has a pulse lengthsufficiently close to a precession period of the domain wall motion andif the at least one current pulse comprises at least two current pulsesthen the current pulses are separated from each other by a pulseinterval sufficiently close to the precession period such that:

the at least one current pulse is configured to cause a depinning of thedomain wall such that the domain wall moves with sufficient energy toescape the spatial confinement; and

each current pulse has an amplitude less than the minimum amplitude of adirect current that would cause said depinning if the direct currentwere applied to the domain wall instead of the at least one currentpulse.

The present invention provides a structure, comprising:

a domain wall that is in spatial confinement by a pinning potential towithin a local region of a magnetic device; and

at least one current pulse applied to the domain wall,

wherein each current pulse has a pulse length in a range of 25% to 75%of a precession period of the domain wall motion and if the at least onecurrent pulse comprises at least two current pulses then the currentpulses are separated from each other by a pulse interval in the range of25% to 75% of the precession period, and

wherein the applied at least one current pulse is configured to cause adepinning of the domain wall such that the domain wall moves withsufficient energy to escape the spatial confinement.

The present invention provides a method and structure for moving thedomain wall away from the potential well to no longer be spatiallyconfined by the potential well, by using less applied energy than ispresently used in the related art.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is comprised of FIGS. 1A and 1B, and represents a schematicillustration of an exemplary operating environment in which a magneticshift register system of the present invention can be used.

FIG. 2 is comprised of FIGS. 2A, 2B, and 2C and represents a schematicdiagram illustrating a method of operation of the magnetic shiftregister of FIG. 1.

FIG. 3 is a process flow chart illustrating a method of operation of themagnetic shift register of FIG. 1.

FIG. 4 is comprised of FIGS. 4A and 4B, and represents a schematicdiagram illustrating an embodiment of the magnetic shift register ofFIG. 1 constructed of multiple types of alternating ferromagneticmaterials.

FIG. 4C is a schematic diagram of another embodiment of the shiftregister of FIG. 1, illustrating a well or bottom section of the shiftregister as being composed of a single ferromagnetic material.

FIG. 5 depicts different configurations for domain walls such thatelectrical current is flowing along a nanowire, in accordance withembodiments of the present invention.

FIG. 6A depicts a magnetization profile for a head-to-head transversewall showing the definition of the x, y, and z axes of a rectangularcoordinate system, in accordance with embodiments of the presentinvention.

FIG. 6B illustrates a definition of the azimuthal angle θ and the tiltangle Ψ in spherical coordinates for describing the direction of themagnetization vector, in accordance with embodiments of the presentinvention.

FIG. 7 illustrates the geometric notation that characterizes the domainwall and the pinning potential, in accordance with embodiments of thepresent invention.

FIGS. 8A-8C depict precessional motion of a domain wall within apotential well for a current of amplitude corresponding to a spin torqueof 510 m/s, in accordance with embodiments of the present invention.

FIGS. 9A-9C depict for the same values of parameters as in FIGS. 8A-8C,precessional motion of a domain wall within a potential well for currentjust below (of amplitude corresponding to spin torque of 510 m/s) andabove (of amplitude corresponding to spin torque of 520 m/s) thethreshold current for depinning, in accordance with embodiments of thepresent invention.

FIGS. 10A and 10B depict for the same values of parameters as in FIGS.8A-8C and 9A-9C, domain wall position and tilt angle versus time for acurrent of amplitude corresponding to a spin torque of 290 m/s, inaccordance with embodiments of the present invention.

FIGS. 11A and 11B depict a comparison of the domain wall position versustime (FIG. 11A) for corresponding dc current and sequences of 1 through5 pulses, for a pulse amplitude corresponding to a spin torque of 75 m/s(FIG. 11B), in accordance with embodiments of the present invention.

FIGS. 12A and 12B depict a comparison of the domain wall position versustime for a sequence of 4 pulses with same polarity (FIG. 12A) and 4½bipolar pulses (FIG. 12B), with a pulse amplitude corresponding to aspin torque of 45 m/s, in accordance with embodiments of the presentinvention.

FIGS. 13A and 13B depict a comparison of the domain wall position versustime for various configurations of pulse length and pulse interval, forsequences of 5 pulses with a current amplitude corresponding to a spintorque of 75 m/s, in accordance with embodiments of the presentinvention.

FIGS. 14-17 are plots of threshold current and reduction thereof versusvarious parameters, in accordance with embodiments of the presentinvention.

FIG. 18A depicts a map of differently shaded regions, said map showing ahead-to-head transverse domain wall, obtained using micromagneticsimulation for a 100 nm wide, 5 nm thick permalloy nanowire, inaccordance with embodiments of the present invention.

FIG. 18B is a plot of dc critical current for domain wall motion as afunction of magnetic field for the domain wall of FIG. 18A, inaccordance with embodiments of the present invention.

FIGS. 19A and 19B depicts magnetization plots resulting frommicromagnetic simulations, in accordance with embodiments of the presentinvention.

FIG. 20A and FIG. 20B respectively depict domain wall position andelectrical current profile versus time from micromagnetic simulationscalculated with a current of 1 mA for various sequence of pulses, inaccordance with embodiments of the present invention.

FIG. 21 depicts critical voltage for domain wall motion as a function ofapplied magnetic field, for 160 pulses, in accordance with embodimentsof the present invention.

FIG. 22 depicts minimum applied magnetic field required for depinningdomain wall motion with a probability larger than 50%, as a function ofthe number of pulses, for a pulse amplitude of 1.2V, in accordance withembodiments of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention provides a method and associated structure formoving magnetic domain walls by using a sequence of synchronized currentpulses.

Spin-polarized currents cause the precession of the magnetization of adomain wall trapped in a pinning potential, as a consequence of aspin-transfer torque mechanism. Such a precession occurs for excitationcurrents smaller than a threshold current (i.e., minimum current)required to move the domain wall outside of the pinning potential withcontinuous current or in the limit of sufficiently long current pulses.In this case, the amplitude of the domain wall oscillation is maximumafter a time of the order of half the intrinsic precession period of thedomain wall. This precession period is a function of the characteristicsof the domain wall and the pinning potential. For longer times, Gilbertdamping causes the amplitude of motion to decrease progressively.

In accordance with embodiments of the present invention, a series ofcurrent pulses are applied in synchronization with the precession periodof the domain wall, resulting in a resonant amplification embodied in anincrease in the amplitude of the precession. This resonant amplificationmay lead to a strong reduction of the threshold current for domain wallmotion by more than one order of magnitude. The reduction of thethreshold current is achieved both with a series of pulses of the samepolarity, separated by intervals with zero current (unipolar pulses),and a series of pulses of alternate polarity (bipolar pulses). Forunipolar pulses, the maximum reduction of the threshold current isobtained when both the pulse length (i.e., duration of individual pulse)and pulse interval (i.e., time between successive pulses) are about halfthe domain wall precession period. For bipolar pulses, the length ofboth the positive and negative portions of the pulses is also about halfthe domain wall precession period. Significant reduction of thethreshold current for domain wall motion is achieved even with a smallnumber of pulses. The present invention is supported by analyticalcalculations, micromagnetic modeling, and experiments.

The detailed description of the present invention comprises sectionsthat describe: (1) a magnetic shift register with a spatially varyingdistribution of magnetic layers to illustrate the pinning of domainwalls; (2) an analytical model for reducing the threshold current toovercome the pinning potential by domain wall motion; (3) quantitativeresults from use of the analytical model; (4) micromagnetic simulations;and (5) experimental support for the analytical model.

1. Magnetic Shift Register with Pinning Potential

FIG. 1 (FIGS. 1A and 1B) illustrates an exemplary high-levelarchitecture of a magnetic memory system 100 comprising a magnetic shiftregister 10 that utilizes a writing device (also referred to herein aswriting element) 15 and a reading device (also referred to herein asreading element) 20. Both the reading device 20 and the writing device15 form a read/write element of system 100.

The magnetic shift register 10 comprises a fine track 11, called“racetrack memory”, made of ferromagnetic material. The track 11 can bemagnetized in small sections, or domains, in one direction or another.Information is stored in regions such as domains 25, 30 in the track 11.The order parameter of the magnetic material from which the track isfabricated, which is the magnetization direction or the direction of themagnetic moment, changes from one direction to another. This variationin the direction of the magnetic moment forms the basis for storinginformation in the track 11.

In one embodiment, the magnetic shift register 10 comprises a dataregion 35 and a reservoir 40. The data region 35 comprises a contiguousset of domains such as domains 25, 30 that store data. Additional lengthis provided to the magnetic shift register 10 in the form of a reservoir40.

The reservoir 40 is made sufficiently long so that it accommodates allthe domains in the region 35 when these domains are moved completelyfrom region 35 across the writing and reading elements for the purposesof writing and reading domains into region 40. At any given time, thedomains are thus stored partially in region 35 and partially in region40 so it is the combination of region 35 and region 40 that forms thestorage element. In one embodiment, the reservoir 40 is wherein thereservoir region is devoid of magnetic domains in a quiescent state.

Thus, the storage region 35 at any given time may be located within adifferent portion of the magnetic shift register 10 and the reservoir 40would be divided into two regions on either side of the storage region35. Although the storage region 35 is one contiguous region, and in oneembodiment of this application the spatial distribution and extent ofthe domains within the storage region 35 would be approximately the sameno matter where the storage region 35 resides within the shift register10, in another embodiment portions of the storage region may be expandedduring the motion of this region particularly across the reading andwriting elements. A portion or all of the data region 35 is moved intothe reservoir 40 to access data in specific domains.

The reservoir 40 is shown in FIG. 1 as approximately the same size asthe data region 35. However, other alternative embodiments may allow thereservoir 40 to have a different size than the data region 35. As anexample, the reservoir 40 could be much smaller than the data region 35if more than one reading and writing element were used for each magneticshift register. For example, if two reading and writing elements wereused for one shift register and were disposed equally along the lengthof the data region, then the reservoir would only need to beapproximately half as long as the data region.

An electric current 45 is applied to the track 11 to move the magneticmoments within domains 25, 30, along the track 11, past the readingdevice 20 or the writing device 15. In a magnetic material with domainwalls, a current passed across the domain walls moves the domain wallsin the direction of the current flow. As the current passes through adomain, it becomes “spin polarized”. When this spin polarized currentpasses through into the next domain across the intervening domain wall,it develops a spin torque. This spin torque moves the domain wall. Thedirection of motion of the domain walls depends on the magnetic materialand the domain walls may move in the direction of the current flow or inthe opposite direction (i.e., the direction of the flow of electrons).The direction of motion is not important for the purposes of theracetrack memory. Domain wall velocities can be very high; e.g., on theorder of 100 m/sec, so that the process of moving a particular domain tothe required position for the purposes of reading this domain or forchanging its magnetic state by means of the writing element can be veryshort.

The domains, such as domains 25, 30, 31 are moved (or shifted) back andforth over the writing device 15 and reading device 20, in order to movethe data region 35 in and out of the reservoir 40, as shown in FIG. 2(FIGS. 2A, 2B, 2C). In the example of FIG. 2A, the data region 35 couldinitially reside on the left side of the well, i.e., bottom section 32,of the magnetic shift register 10, with no domains in the reservoir 40.FIG. 2C shows the case where the data region 35 resides entirely on theright side of the magnetic shift register 10.

In order to write data in a specific domain, such as domain 31, acurrent 45 is applied to the magnetic shift register 10 to move domain31 over, and in alignment with the writing device 15. All the domains inthe data region 35 move when the current is applied to the magneticshift register.

The movement of the domains is controlled by both the amplitude anddirection (i.e., polarity) of the current, and the time over which thecurrent is applied. In one embodiment, one current pulse of a specifiedshape (amplitude versus time) and duration is applied to move thedomains in the storage region in one increment or step. A series ofpulses are applied to move the domains the required number of incrementsor steps. Thus, a shifted portion 205 (FIG. 2B) of the data region 35 ispushed (shifted or moved) into the reservoir region 40. The direction ofmotion of the domains within the track 11 depends on the direction ofthe applied current.

In order to read data in a specific domain, such as domain 25,additional current is applied to the magnetic shift register 10 to movedomain 25 over, and in alignment with the reading device 20. A largershifted portion 210 of the data region 35 is pushed (shifted or moved)into the reservoir 40.

The reading and writing devices shown in FIGS. 1 and 2 form part of acontrol circuit that defines a reference plane in which the reading andwriting devices are arrayed. In one embodiment, the magnetic shiftregister 10 stands vertically out of this reference plane, largelyorthogonal to this plane.

In order to operate the magnetic shift register 10, the control circuitincludes, in addition to the reading and writing elements, logic andother circuitry for a variety of purposes, including the operation ofthe reading and writing devices, the provision of current pulses to movethe domains within the shift register, the means of coding and decodingdata in the magnetic shift register, etc. In one embodiment the controlcircuit is fabricated using CMOS processes on a silicon wafer. Themagnetic shift registers will be designed to have a small footprint onthe silicon wafer so as to maximize the storage capacity of the memorydevice while utilizing the smallest area of silicon to keep the lowestpossible cost.

In the embodiment shown in FIG. 1, the footprint of the shift registerwill be determined largely by the area of the wafer occupied by thereading and writing devices. Thus, the magnetic shift register will becomprised of tracks extending largely in the direction out of the planeof the wafer. The length of the tracks in the vertical direction willdetermine the storage capacity of the shift register. Since the verticalextent can be much greater than the extent of the track in thehorizontal direction, hundreds of magnetic bits can be stored in theshift register yet the area occupied by the shift register in thehorizontal plane is very small. Thus, the shift register can store manymore bits for the same area of silicon wafer as compared to conventionalsolid state memories.

Although the tracks of the magnetic shift register are shown as beinglargely orthogonal to the plane of the reading and writing elements (thecircuitry plane) these tracks can also be inclined, at an angle, to thisreference plane, as an example, for the purpose of greater density orfor ease of fabrication of these devices.

A method 300 of operating the magnetic shift register 10 is illustratedin FIG. 3, with further reference to FIG. 2 (FIGS. 2A, 2B, and 2C). Forillustration purpose, a memory system 100 utilizing the magnetic shiftregister 10 wishes to either read the data in domain 25 or write data todomain 25 (refer to FIG. 2A).

At block 305, the memory system 100 determines the number of bitsrequired to move domain 25 to either the writing device 15 or readingdevice 20. The memory system 100 also determines the direction requiredto move domain 25 in bock 310. In FIG. 2A, domain 25 is on the left ofthe writing device 15 and the reading device 20. A positive current 45might be required to move domain 25 to the right, for example, while anegative current 45 might be required to move domain 25 to the left.

The memory system 100 then applies the desired current 45 to themagnetic shift register 10 at block 315. Current 45 may be one pulse ora series of pulses, moving the domain 25 one bit at a time. It is alsopossible to vary the length of duration or the amplitude of the currentwithin the pulse or the pulse shape (current versus time within thepulse), to cause the domain 25 within the storage region 35 to move byseveral increments during the application of one pulse. The domains inthe data region 35 move in response to the current 45 in block 320.Domain 25 stops at the desired device, i.e., writing device 15 orreading device 20 (block 325).

With reference to FIG. 4 (FIGS. 4A, 4B), an alternative magnetic shiftregister 10A may be constructed similarly to the shift register 10 ofFIGS. 1 and 2, but made of alternating magnetic layers, to pin thepossible locations of the domains within the magnetic shift register10A. Pinning the possible locations of the domains prevents thedesignated domains from drifting.

The magnetic layers may be comprised of various ferromagnetic orferrimagnetic materials where these magnetic materials are chosenappropriately based primarily on the magnitude of their magnetization(magnetic moment per unit volume), exchange parameter, magneticanisotropy, and damping coefficient. The choice of these materials willalso be influenced by their manufacturability and compatibility with theprocess used to fabricate the magnetic shift register.

As shown in region 405 of the shift register 10A, one type of magneticmaterial may be used for domains 410, 420, while a different type ofmagnetic material may be used for alternating domains 415, 425. Inanother embodiment, multiple types of magnetic materials may be used, invarying order of materials.

The introduction of different ferromagnetic layers in the magnetic shiftregister 10A creates local energy minima, similar to “potential wells”,so that the domain walls between domains of opposite polarity will alignthemselves with the boundaries between the alternating ferromagneticlayers 410, 415, etc. Thus, the extent and size of the domains will bedetermined by the thicknesses of the magnetic layers.

A current pulse 45 applied to the magnetic shift register 10A causes thedomains 410-425 within the region 405 to move in the direction of thecurrent 45. However, unless the current pulse 45 is of sufficientamplitude and duration, the domains 410-425 may not move past theboundaries between the two different types of magnetic material.Consequently, the data region 35 can be moved one bit at a time, and thedomains are not allowed to drift past their desired positions.

In addition to pinning the possible locations of the domains, usingdifferent layers of magnetic material also allows higher tolerances forcurrent amplitude and pulse duration. In this embodiment, the portion ofthe magnetic shift register 10A that passes over the writing device 15and the reading device 20 can be a homogeneous magnetic material orlayers of different magnetic materials as illustrated in FIG. 4C.

The length of the alternating magnetic regions 410, 420, etc. and 415,425 etc. can be different. Moreover, although it may be preferred thatthe length of each type of magnetic region 410, 420, etc., and 415, 425,etc. be the same throughout the shift register, this is not essential,and these lengths can vary somewhat throughout the magnetic shiftregister. What is important is the potential that pins the domains intheir defined positions against current induced motion induced by thecurrent pulses.

2. Analytical Model

An analytical model used by the present invention is based upon aone-dimensional model of domain walls, which includes the effect ofspin-polarized currents flowing across the domain wall. Thesespin-polarized currents exert torques on the magnetization.

FIG. 5 depicts different configurations for domain walls such thatelectrical current is flowing along a nanowire in a direction 51 (xdirection), in accordance with embodiments of the present invention. InFIG. 5, the magnetization directions 56 and 57 of two neighboringmagnetic domains 53 and 54, respectively, are separated by a magneticdomain wall 52 across which the magnetization rotates from one direction56 to the other 57. In FIG. 5, the magnetization directions 56 and 57are shown schematically for: (a) a Néel wall configuration; (b) a Blochwall configuration; and (c) a head-to-head wall configuration. In FIG. 5the cross-section of the nanowire is such that the nanowire is wider inthe direction y within the plane shown in FIG. 5 (and perpendicular tothe current direction x) and thinner in the direction z perpendicular tothe plane illustrated in FIG. 5.

FIG. 6A depicts a magnetization profile for a head-to-head transversewall showing the definition of the x, y, and z axes of a rectangularcoordinate system, in accordance with embodiments of the presentinvention. FIG. 6B illustrates a definition of the azimuthal angle θ andthe tilt angle Ψ for describing the magnetization direction 55 inspherical coordinates, in accordance with embodiments of the presentinvention. The nanowire's long axis is along the x axis and the nanowireis in the (x,y) plane.

2.1 One-Dimensional Model

A one-dimensional model assumes a particular form of the configurationof the magnetization directions within a domain wall. In theone-dimensional model the magnetization direction only varies along onedirection, namely the direction x. In a quiescent state, in which thereis an absence of any corresponding spin torque of perturbation (e.g.,there is no electrical current along the nanowire and no externalmagnetic field), the angles θ and Ψ characterizing the magnetizationdirection 55 within the domain wall are described by Equations (1A) and(1B):θ(x)=±2 arctan(e ^((x-q)/Δ))  (1A)Ψ(x)=C  (1B)wherein q(t) is the position of the domain wall center along x as afunction of time, Ψ(x) is the tilt angle of the domain wallmagnetization away from its equilibrium position as a function of x, andΔ is the domain wall width parameter. C is a constant whose value iszero for a Bloch wall and a Head to Head transverse wall and is π/2 fora Néel wall. In the following discussion only the case of the Head toHead wall is considered in detail.

Note that Equations (1A) and (1B) are exact for the one-dimensionalBloch wall configuration (b) of FIG. 5. The one-dimensional model alsoprovides a good description of the Néel wall configuration (a) and thehead-to-head transverse wall configuration (c) of FIG. 5. Qualitativeagreement is also obtained for more complex domain wall configurations(for example, the head-to-head vortex wall).

The domain wall width parameter for a transverse wall is written as:

$\begin{matrix}{{\Delta = {\Delta_{0}/\sqrt{1 + {\frac{K}{K_{0}}{\sin^{2}(\Psi)}}}}}{\Delta_{0} = \sqrt{\frac{A}{K_{0}}}}} & (2)\end{matrix}$wherein A is the exchange constant (which is ˜10⁻⁶ erg/cm for permalloy)and K₀ is the magnitude of the uniaxial anisotropy, and K is themagnitude of the transverse anisotropy.

The uniaxial anisotropy K₀ defines the easy direction of magnetizationin the nanowire and, thereby, the preferred direction of themagnetization within the magnetic domains, wherein the magnetizationdirection is parallel to the wire long axis in the case of head-to-headdomain walls (see (c) in FIG. 5), in-plane perpendicular to the wirelong axis in the Neel geometry (see (a) in FIG. 5), and perpendicular tothe nanowire plane in the Bloch geometry (see (b) in FIG. 5).

In the head-to-head configuration, the transverse anisotropy K islocated in the plane of the wire perpendicular to the wire long axis.The magnitude of the transverse anisotropy K can also be written as ananisotropy field H_(k)=2K/M_(S), where M_(S) is the saturationmagnetization of the material. For soft magnetic materials (for example,permalloy) and in the case of a transverse wall in the head-to-headconfiguration, the transverse anisotropy K is related to the aspectratio of the cross-section of the nanowire.

For simplicity, it is assumed herein that K₀>>K, such that the domainwall width parameter is essentially constant throughout the motion ofthe domain wall.

2.2 Pinning of the Domain Wall and External Field

A parabolic pinning potential describes the experimental pinning of thedomain wall in nanowires. The pinning can be either a weak pinningassociated with random defects and edge roughness, or a stronger pinningat a lithographically designed pinning site (e.g., notch, hump, step,etc.) or in a nanowire formed of alternating magnetic materials. Thecase of random defects within the interior or at the edges or surfacesof the nanowire may especially be the case for a nanowire formed from ahomogeneous magnetic material with no engineered defects or pinningsites. The parabolic pinning potential σ(q) is defined as follows:σ(q)=Vq ₀(q/q ₀)² for |q|<q ₀  (3)σ(q)=Vq ₀ for |q|>q ₀wherein σ is the potential energy of the domain wall per unit surfacearea (erg/cm²), V is the depth of the potential (dimension of an energydensity erg/cm³), and q₀ is the spatial extension of the potential. Theposition q corresponds to the position of the center of the domain wallrelative to the center of the pinning potential. Thus q=0 corresponds tothe center of the pinning potential.

FIG. 7 illustrates the geometric notation that characterizes the domainwall and the pinning potential, in accordance with embodiments of thepresent invention. In FIG. 7, domain wall 65 is disposed between domains64 and 66. The pinning potential 60 extends over a length of scale q₀.The center 67 of the domain wall 65 has a position q relative to thecenter 62 of the pinning potential 60. FIG. 7 depicts the embodiment of|q|<q₀ in Equations (3).

Note that q₀ is not the physical size of the pinning feature, but ratheris the extension of the potential well which reflects both the size ofthe feature (e.g., notch) and the width of the domain wall.

Magnetic fields applied along the nanowire (parallel to the direction ofthe magnetization in the domains for the head to head domain wallconfiguration) exert a pressure on the domain wall which can be includedin the domain wall potential energy. In the presence of such an appliedmagnetic field H, the contribution to the domain wall potential energyis −2M_(S)Hq.

2.3 Equations of Motion

Within the framework of the one-dimensional approximation, the dynamicsof the domain wall can be described by the two variables q(t) and Ψ(t).The equations of motion for q(t) and Ψ(t) are as follows:

$\begin{matrix}{{( {1 + \alpha^{2}} )\overset{.}{q}} = {{{{- \frac{\alpha\;\gamma\;\Delta}{2\; M_{S}}}( \frac{\partial\sigma}{\partial q} )} + {\frac{\gamma\;\Delta}{2}H_{k}{\sin( {2\;\Psi} )}} + {( {1 + {\alpha\;\beta}} ){u( {1 + \alpha^{2}} )}\overset{.}{\Psi}}} = {{{- \frac{\gamma}{2\; M_{S}}}( \frac{\partial\sigma}{\partial q} )} - {\frac{\gamma\;\alpha}{2}H_{k}{\sin( {2\;\Psi} )}} + \frac{( {\beta - \alpha} )u}{\Delta}}}} & (4)\end{matrix}$wherein α is the Gilbert damping (dimensionless), M_(s) is thesaturation magnetization of the material, and γ is the gyromagneticratio (17.6 MHz/Oe). In the following calculations and simulations, thevalue of M_(s) for permalloy (800 emu/cm³) is used.

The influence of current on the domain wall dynamics is characterized bythe two parameters u (dimension of a velocity, m/s) and β(dimensionless).

The parameter u is the magnitude of the spin-transfer torque which isproportional to the current density J in the nanowire and is derivedfrom the conservation of the spin angular momentum. The parameter u iswritten:u=gμ _(B) JP/2eM _(S)  (5)wherein g is the Lande factor (˜2), J is the current density, P is thespin-polarization of the current, μ_(B) is the Bohr magneton(0.927×10⁻²⁰ emu), and e is the electron charge (1.6×10⁻¹⁹ C).

The spin polarization P may be less than 1 and depends on the material.Using a value of P=0.4 for permalloy in Equation (5), the ratio ofcurrent density J to the spin torque amplitude u is about 3.5 10⁶ A/cm²to 1 m/s. Also note that in some models, the polarization P is replacedby the Slonczewski function g(P) in Equation (5), in which case theratio of the current density J to the spin torque amplitude is about 2.410⁶ A/cm² for 1 m/s. See J. C. Slonczewski, J. Magn. Magn Mater. 159, L1(1996) for a discussion of the Slonczewski function g(P).

The discussion infra of current density J and associated numericalresults is expressed under a convention that a unit current flow area of1 cm² is used, so that 1 ampere (“A”) of electrical current through anarea of 1 cm² corresponds to 1 A/cm² of current density. In thefollowing, references to “current” refer to current flowing through ananowire with an area A so that the current density would be the currentdivided by the area A. Thus in the discussions infra, in light of thefact that spin torque u is related to current density J via Equation(5), indications of electrical current expressed in units of m/sec referto an electrical current density J that induces a spin torque u of theexpressed units of m/sec in the ferromagnetic material normalized,independent of the cross-sectional area, for the same current density J.

The parameter β in Equation (5) characterizes a force on the domain wallwhich may be exerted by the spin-polarized current in addition to thespin-transfer torque. The magnitude of β is of the order of the Gilbertdamping constant α. See the following references for discussions of theorigin and magnitude of β: Gen Tatara and Hiroshi Kohno, Phys. Rev.Lett. 92, 086601 (2004); A. Thiaville, Y. Nakatani, J. Miltat and Y.Suzuki, Europhys. Lett., 69, 990 (2005); S. E. Barnes and S. Maekawa,Phys. Rev. Lett. 95, 107204 (2005); and S. Zhang and Z. Li, Phys. Rev.Lett. 93, 127204 (2004).

3. Quantitative Results from Use of the Analytical Model

3.1 Current-Driven Precessional Motion of Domain Wall Trapped inParabolic Potential

A domain wall submitted to a current below the threshold current fordepinning undergoes a precessional motion within the potential well.FIGS. 8A-8C (collectively “FIG. 8”) depict such precession in terms ofthe domain wall position q versus time (FIG. 8A), domain wall tilt angleΨ versus time (FIG. 8B), and the phase space (q,Ψ) (FIG. 8C), inaccordance with embodiments of the present invention. In FIG. 8, thedomain wall precession is driven by an electrical current correspondingto a spin torque u of 510 m/s (just below the critical current),calculated numerically using the one dimensional model of Equations (4).The parameters of the calculations are Δ=100 nm, H_(k)=800 Oe, V=10⁵erg/cm³, q₀=100 nm, α=0.01, β=0.01 and H=0.

The period (t_(osc)) of the precessional motion of the domain wall canbe derived analytically in the zero-damping limit by linearizingEquations (4) for small amplitude oscillations and using the parabolicpinning potential of Equation (3), resulting in Equation (6):t _(osc)=2π/γ(M _(S) q ₀ /VH _(k)Δ)^(1/2)  (6)

Generally the precession period is a function of ∂σ/∂q and may thereforevary dynamically with spatial position of the domain wall. For highamplitude oscillations (i.e., nonlinear oscillations), the precessionperiod increases slightly with current.

As shown in FIG. 8, the amplitude of the oscillations is damped by theGilbert damping. Therefore, the maximum amplitude of motion (both in qand Ψ) is reached at short times during the first orbit of theprecession, which can be seen in FIG. 8C wherein the domain walltrajectory is plotted in the phase space (q,Ψ).

Current-driven depinning occurs when the domain wall trajectory exitsthe potential well. For long pulses or dc currents, depinning shouldoccur during the first orbit of precession where the domain walldisplacement is maximum. The dc critical current (i.e., thresholdcurrent) for depinning can be determined numerically, and can also becalculated analytically in the zero-damping limit. The dc thresholdcurrent for depinning in the example of FIG. 8 is determined numericallyto be 516 m/s. Using analytical Equations (7)-(8) discussed infra, aslightly smaller value 507 m/s is obtained, because of the zero-dampingapproximation.

FIGS. 9A-9C (collectively “FIG. 9”) depict precessional motion of adomain wall within a potential well for electrical current just belowthe threshold current for depinning (u=510 m/s, curves 71-73) and justabove the threshold current for depinning (u=520 m/s, lines 74-76), inaccordance with embodiments of the present invention. The plots in FIG.9 are: q versus time (FIG. 9A), Ψ versus time (FIG. 9B), and Ψ versus q(FIG. 9C). In the example of FIG. 9, this dc critical currentcorresponds to a spin torque u of 520 m/s. In FIG. 9, the parameters ofΔ, H_(k), V, q₀, α, β, and H have the same numerical values as in FIG. 8and the plots for current just below the threshold current are the sameas in FIG. 8.

The dc threshold current for domain wall motion has been determinedanalytically in the zero damping limit and the following two differentmechanisms for depinning are utilized in the present invention, forwhich the threshold currents are written as:u _(c1)=γ(VH _(k) Δq ₀ /M _(S))^(1/2)  (7)u_(c2)˜0.36γH_(k)Δ  (8)The actual threshold current is the smallest of u_(c1) and u_(c2). Theseexpressions in Equations (7) and (8) correspond to the thresholddepinning current for two different regimes of depinning, field-like(when the domain wall position q exceeds the pinning potential width q₀during the domain wall's oscillatory trajectory) and current-like (whenΨ exceeds the bifurcation point; i.e. when Ψ exceeds a critical valuesuch that the domain wall's trajectory no longer follows an oscillatorypath) and are derived for the zero-field case without damping and forβ=0.

Sections 3.2-3.4 describe the effect of current pulses on the thresholdcurrent for depinning. The rise and fall times of the current pulses areeach assumed to be less than about 25% of the domain wall precessionperiod.

3.2. Current Pulses: Inertia Driven Depinning.

If the current amplitude is smaller than the threshold current fordepinning, then during the current pulse, the domain wall undergoes aprecessional motion in accordance with Equations (4). When the currentis turned off, this precession continues as the domain wall precessestowards its equilibrium state without current. Depending upon the lengthof the current pulse and the position of the domain wall in the (q,Ψ)phase space when the current is turned off, the amplitude of the domainwall oscillations after the end of the current pulse can increase,leading to depinning of the domain wall after the current is turned off.The amplitude of the domain wall oscillations, after the end of thecurrent pulse, is maximum when the current pulse length is about halfthe domain wall precession period for the case of a current pulseshorter than the precessional period of the domain wall. For currentpulses longer than the precessional period of the domain wall, theamplitude of the domain wall oscillation after the end of the currentpulse is maximized when the current pulse length is equal to an integernumber of oscillation periods plus about half an oscillation period.

FIGS. 10A and 10B (collectively “FIG. 10”) depict for the same values ofparameters (Δ, H_(k), V, q₀, α, β, H) as in FIGS. 8 and 9, domain wallposition q versus time (FIG. 10A) and Ψ versus q (FIG. 10B) for acurrent of amplitude corresponding to a spin torque u of 290 m/s, in thecase of a dc current (curves 81-82) and a pulse current of 0.6 nsduration (curves 84-85), in accordance with embodiments of the presentinvention.

In the example shown in FIG. 10, the domain wall exits the potentialwell for a current pulse of amplitude corresponding to a spin torqueu=290 m/s with a duration of 0.6 ns, whereas it stays within thepotential well for a dc current of the same amplitude. The dc criticalcurrent for depinning of about 516 m/s is thus reduced by a factor ofabout 1.8 (i.e., 516/290) when a single current pulse is used instead ofa dc current.

Note that domain wall motion can occur after several periods ofprecession if the domain wall momentum is large enough, leading tooscillations in the critical current as a function of current pulselength.

3.3 Series of Pulses: Resonant Depinning

The domain wall can be driven into resonance when a series of currentpulses is used. This leads to a further amplification of the domain walloscillations after the end of the train of current pulses and, thereby,a further reduction in the critical current for depinning the domainwall. This amplification of the amplitude of the precessionaloscillatory motion is illustrated in FIGS. 11A and 11B (collectively“FIG. 11”) which depict a comparison of the domain wall position qversus time (FIG. 11A) for corresponding dc current and sequences of 1through 5 current pulses (FIG. 11B), in accordance with embodiments ofthe present invention. In FIG. 11, the current amplitude corresponds toa spin torque u of 75 m/s (about 7 times smaller than the dc thresholdcurrent of 516 m/s). The individual pulse lengths and the time intervalsbetween individual pulses are 0.6 ns. The dotted lines show theboundaries of the potential well (±100 nm). The calculation parameters(Δ, H_(k), V, q₀, α, β, H) have the same numerical values as in FIG. 8.

The amplification of the precession leads to domain wall depinning forthis current value for a sequence of 5 pulses of the same polarity, butnot for the dc nor for the 1, 2, 3, and 4 pulse sequences. Both thelength and the interval between the pulses is about half the precessionperiod. The precession period is 1.2 ns.

FIGS. 12A and 12B (collectively “FIG. 12”) depict a comparison of thedomain wall position q versus time for a sequence of 4 pulses with thesame polarity (FIG. 12A) and 4½ bipolar pulses (FIG. 12B), with acurrent pulse amplitude corresponding to a spin torque u of 45 m/s, inaccordance with embodiments of the present invention. The dotted linesshow the boundaries of the potential well (±100 nm). Also shown is thecurrent profile versus time (top panel in each of FIGS. 12A and 12B).The calculation parameters (Δ, H_(k), V, q₀, α, β, H) have the samenumerical values as in FIG. 8.

As shown of FIG. 12, domain wall motion is achieved for a currentcorresponding to a spin torque u of 45 m/s with a sequence of 4 bipolarpulses. This corresponds to a reduction by more than one order ofmagnitude (i.e., by more than a factor of 10) compared to the dcthreshold current corresponding to a spin torque of 516 m/s. In thisexample, the reduction in threshold current is a factor of about 12(i.e., 516/45).

This strong reduction of threshold current for domain wall depinning ischaracterized by the domain wall being driven into resonance by tuningboth the length of the pulses and the interval between the pulses to beabout half the precession period of the domain wall motion.

FIGS. 13A and 13B (collectively “FIG. 13”) depict a comparison of thedomain wall position q versus time for various configurations of pulselength and pulse interval for sequences of 5 pulses with a currentamplitude corresponding to a spin torque u of 75 m/s, in accordance withembodiments of the present invention. FIG. 13A depicts both pulse lengthand pulse intervals being the same, namely 0.5 ns, 0.6 ns, and 0.7 ns,from top to bottom, respectively. FIG. 13B depicts constant pulse length(0.6 ns) and increasing pulse intervals, namely 0.3 ns, 0.6 ns, and 1.2ns, from top to bottom, respectively. The dotted lines show theboundaries of the potential well (+100 nm). The calculation parameters(Δ, H_(k), V, q₀, α, β, H) have the same numerical values as in FIG. 8.

As shown in FIG. 13, for the same sequence of 5 unipolar pulses withcurrent amplitude corresponding to a spin torque u of 75 m/s, domainwall motion is only achieved when both the pulses length and theinterval between the pulses is 0.6 ns, which is about half theprecession period of the domain wall motion. Similarly, for bipolarpulses, resonance is achieved when the pulse length for both positiveand negative currents is about half the precession period of the domainwall motion.

Based on the preceding discussion relating to FIGS. 10-13 with respectto using current pulses for depinning domain wall motion, the requiredcurrent amplitude for depinning the domain wall motion is minimal if thepulse length and the interval between the pulses is about half theprecession period of the domain wall motion.

3.4 Mapping of the Parameter Space

FIGS. 14-17 are plots of threshold current and reduction thereof versusvarious parameters, in accordance with embodiments of the presentinvention. The threshold current facilitates domain wall motion outsideof the pinning potential. The parameters in FIGS. 14-17 are: transverseanisotropy field H_(k) (FIGS. 14A and 14B), domain wall width parameterΔ (FIGS. 15A and 15B), pinning potential width q₀ (FIGS. 16A and 16B),and pinning potential depth V (FIGS. 17A and 17B). FIGS. 14A, 15A, 16A,and 17A depict a plot of threshold current for the embodiments of: dccurrents (solid squares), a single pulse with a length half theprecession period (solid circles), and a sequence of 4½ bipolar pulsesat resonance (solid diamonds). FIGS. 14A, 15A, 16A, and 17A also depictoptimal pulse length for achieving maximum threshold current reduction(open squares, right axis of the figures) as well as half of theprecession period from the analytical expression given by Equation 6(dashed curve 89). FIGS. 14A, 15A, 16A, and 17A also depict the curves87 and 88 representing the analytical expressions of the criticalthreshold current u_(c1) and u_(c2) in the two depinning regimes ofEquations (7) and (8), respectively. FIGS. 14B, 15B, 16B, and 17B depictthe ratio of the threshold current for the dc case to the criticalcurrent for the 4½ bipolar pulses at resonance case, said ratiocorresponding to the factor by which the threshold current is reduced ascompared to the dc case.

For FIG. 14, other parameters values employed are: Δ=100 nm, V=10⁵erg/cm³, q₀=100 nm, α=0.01, β=0.01 and H=0.

For FIG. 15, other parameters values employed are: H_(k)=1200 Oe, V=10⁵erg/cm³, q₀=100 nm, α=0.01, β=0.01 and H=0.

For FIG. 16, other parameters values employed are: Δ=100 nm, H_(k)=1200Oe, V=10⁵ erg/cm³, α=0.01, β=0.01 and H=0.

For FIG. 17, other parameters values employed are: Δ=100 nm, H_(k)=1200Oe, q₀=100 nm, α=0.01, β=0.01 and H=0.

FIGS. 14-17 show that for both the single pulse embodiment (solidcircles) and the sequence of 4½ bipolar pulses embodiment (soliddiamonds), the threshold current is reduced relative to the use of dccurrents (solid squares) for all parameters varied. Moreover, thethreshold current reduction exceeded more than one order of magnitudefor a wide range of parameter variations.

The discussions supra in Sections 3.2-3.4 demonstrate that the requiredcurrent amplitude for depinning the domain wall motion is minimal undera resonance condition such that the pulse length and the intervalbetween the pulses is about half the precession period of the domainwall motion. The preceding discussions further demonstrate that the useof current pulses at the resonance condition reduces the requiredthreshold current for depinning domain wall motion relative to athreshold dc current. Therefore, one or more current pulses may be usedto reduce the required threshold current for depinning domain wallmotion relative to use of a dc current at both the resonance conditionor under off-resonance conditions as well. For example, in FIG. 12 theuse of 4 bipolar pulses at resonance reduces the threshold current by afactor of about 12. As the pulse length and the pulse interval in timebetween successive pulses deviates increasingly from one-half theprecession period of the domain wall, the threshold current reductionrelative to a dc current will decrease until said deviation fromresonance (i.e., from one-half the precession period of the domain wallmotion) is sufficiently large that the threshold current reductionrelative to a dc current is substantially zero or negligible. Themaximum permissible deviation from resonance, at which there is apositive threshold current reduction relative to a dc threshold current,is a function of the current pulse configuration (i.e., number ofpulses, unipolar versus bipolar pulses, etc.). The present inventionincludes the following embodiments for using one or more pulses(unipolar or bipolar) within the maximum permissible deviation fromresonance.

The present invention provides a method and structure in which a domainwall is in spatial confinement by a pinning potential to within a localregion of a magnetic device. At least one current pulse is applied tothe domain wall. Each current pulse has a pulse length sufficientlyclose to a precession period of the domain wall motion and if the atleast one current pulse comprises at least two current pulses then thecurrent pulses are separated from each other by a pulse intervalsufficiently close to the precession period such that: the at least onecurrent pulse is configured to cause a depinning of the domain wall suchthat the domain wall moves with sufficient energy to escape the spatialconfinement; and each current pulse has an amplitude less than theminimum amplitude of a direct current (i.e., threshold direct current)that would cause said depinning if the direct current were applied tothe domain wall instead of the at least one current pulse.

The present invention further provides a method and structure in which adomain wall is in spatial confinement by a pinning potential to within alocal region of a magnetic device, subject to at least one current pulseapplied to the domain wall, each current pulse having a pulse length ina range of 25% to 75% of a precession period of the domain wall motion,and if the at least one current pulse comprises at least two currentpulses then the current pulses are separated from each other by a pulseinterval in the range of 25% to 75% of the precession period.

In one embodiment, the pulse length and the pulse interval are each in arange of 25% to 75% of the precession period of the domain wall motion.

In one embodiment, the pulse length and the pulse interval are each in arange of 30% to 70% of the precession period of the domain wall motion.

In one embodiment, the pulse length and the pulse interval are each in arange of 35% to 65% of the precession period of the domain wall motion.

In one embodiment, the pulse length and the pulse interval are each in arange of 40% to 60% of the precession period of the domain wall motion.

In one embodiment, the pulse length and the pulse interval are each in arange of 45% to 55% of the precession period of the domain wall motion.

In one embodiment, the pulse length and the pulse interval are eachabout 50% of the precession period.

In one embodiment, the at least one current pulse comprises at least twocurrent pulses.

In one embodiment, the pulse interval is about equal to the pulselength.

In one embodiment, the at least two current pulses are unipolar pulses.

In one embodiment, the at least two current pulses are bipolar pulses.

In one embodiment, the amplitude of each pulse is less than the directcurrent threshold by more than a factor selected from the groupconsisting of 2, 3, 4, 5, 6, 7, 8, 9, and 10.

In one embodiment, the magnetic device is a magnetic shift registercomprising a track of alternating domains of ferromagnetic material asdiscussed supra in conjunction with FIG. 4, wherein the domain wall isbetween and in direct contact with a first domain and a second domain ofthe alternating domains, and wherein the first domain comprises a firstferromagnetic material and the second domain comprises a secondferromagnetic material that differs from the first ferromagneticmaterial to create the pinning potential.

In another embodiment, the magnetic device is a magnetic shift registercomprising a track of alternating domains of ferromagnetic material asdiscussed supra in conjunction with FIG. 4, wherein the domain wall isbetween and in direct contact with a first domain and a second domain ofthe alternating domains, and wherein the domain wall is located at apinning potential provided in the racetrack memory.

4. Micromagnetic Simulations

Micromagnetic calculations allow for the study of more realistic domainwall structures and their pinning and depinning. Micromagneticsimulations use a finite element method wherein the magnetic system isdivided into small elements (typically cubes 2 to 10 nm on each side),which are small enough to behave as simple macro-spins (i.e., largemagnetic moments) and which interact with one-another through exchangeand magnetostatic forces. The static and dynamic properties of themagnetic system are calculated by solving the Landau-Lifshitz-Gilbert(LLG) equations for each of the magnetic elements. Unlike theone-dimensional model, micromagnetic simulations do not require anyapproximation of the magnetic configuration beyond the use of macro-spinfinite elements. Micromagnetic simulations can account for the fact thatdomain walls are not rigid objects but can be strongly distorted duringtheir motion. Moreover, micromagnetic simulations can also include theeffect of the inhomogeneous self-field created by the electric currentflowing through the nanowire. Micromagnetic simulations are in goodagreement with the findings of the one-dimensional model describedsupra. Micromagnetic simulations permit the precessional motion of thedomain wall pinned at a defect (e.g., a notch) to be observed fornanowires with various dimensions, with both transverse and vortexhead-to-head domain walls. Inertia driven depinning with a single pulsehas been demonstrated, via micromagnetic simulations, for thesedifferent wall structures.

FIG. 18A depicts a map of differently shaded regions, said map showing ahead-to-head transverse domain wall, obtained using micromagneticsimulation for a 100 nm wide, 5 nm thick permalloy nanowire 90, inaccordance with embodiments of the present invention. The arrows 95 and96 indicate the magnetization direction. By removing a small number ofthe finite elements at the bottom edge of the wire (or setting theirmoments to zero) a pinning potential in the form of a notch 94 (10×5nm²) is formed which provides a pinning field of about 27 Oe.

FIG. 18B is a plot of dc critical current for domain wall motion as afunction of an applied magnetic field H for the domain wall 94 of FIG.18A, in accordance with embodiments of the present invention. FIGS. 18Aand 18B are denoted collectively as “FIG. 18”. The damping constant α is0.01, and the non adiabatic spin torque is neglected (β=0). Note that inthe micromagnetic simulations, the other parameters entering theone-dimensional model (Δ, H_(k), V and q₀) are not controlledindependently but rather are determined by the material properties, thewire dimensions, and the notch characteristics.

Micromagnetic simulations have been performed with a constant appliedmagnetic field H=10 Oe. The corresponding dc depinning current is about5.7 mA (1.14 10⁹ A/cm² current density). For dc current smaller than 5.7mA, the domain wall remains trapped at the notch and undergoes a dampedprecessional motion. To compare these oscillations with the onedimensional model, the net magnetization, integrated over all theelements forming the nanowire, may be plotted along the nanowire (M_(x))and perpendicular to the plane of the nanowire (M_(z)). As can been seenin FIG. 6, these two quantities (M_(x) and M_(z)) are a good descriptionof the domain wall position q and the tilt angle Ψ.

An example of this precessional motion, derived from micromagneticsimulations using the preceding conditions (H=10 Oe, α=0.01, β=0), isshown in FIGS. 19A and 19B (collectively “FIG. 19”). FIG. 19A depictsreduced magnetization Mx/Ms 97 and Mz/Ms 98 as a function of time. FIG.19B depicts the associated domain wall trajectory 99 in the phase spacerepresented by the magnetization component (Mz/Ms,Mx/Ms). Thequalitative agreement between the micromagnetic simulations of FIG. 19and the one dimensional model is excellent. See FIG. 8 for comparison.The domain wall precession period obtained from this micromagneticsimulation is about 550 ps. The optimum pulse length should then beabout 275 ps.

FIG. 20A depicts domain wall position versus time from micromagneticsimulations calculated with a current of 1 mA for various sequence ofpulses, shown in FIG. 20B, in accordance with embodiments of the presentinvention. These micromagnetic simulations are performed using thefollowing parameters values: H=10 Oe, α=0.01, β=0. The pulse length usedin these calculations is 280 ps, which is very close to the optimumvalue. For such a small current (i.e., 17.5% of the dc thresholdcurrent), the amplitude of the oscillations is rather small for a dcexcitation. This amplitude increases significantly for a single pulseand a sequence of 2 pulses, and the domain wall eventually exits thenotch after only 3 pulses. This corresponds to a reduction of thecritical current by a factor of 5.7. An even stronger reduction isobtained for bipolar pulses. The critical current is only 0.7 mA for 2½bipolar pulses (factor of 8 reduction).

Micromagnetic simulations exhibit a complex behavior not accessibleusing the one dimensional model. For example, the domain wall can bestrongly distorted during its precession, thus leading to changes in theprecession period and loss of resonance conditions when the number ofpulses increases.

5. Experimental Support for the Analytical Model

FIG. 21 depicts critical voltage for domain wall motion as a function ofan applied external magnetic field H, for 160 pulses, in accordance withembodiments of the present invention. The critical voltage is defined asthe value above which domain wall motion occurs with a probabilitylarger than 50%. Open symbols show a relatively high value of criticalvoltage outside of resonance conditions (pulse length ˜3 ns) and solidsymbols show a significantly reduced critical voltage at the firstresonance (pulse length ˜1.5 ns). It is not possible to estimate thereduction of the critical current at low or zero field in thisexperiment, since no domain wall motion is observed for dc current orwith a single pulse in the voltage range accessible experimentally(i.e., higher voltages would destroy the sample due to excessivecurrents). However, in the presence of an external magnetic field, thecritical current at resonance is reduced by a factor larger than 3.Squares and circles show results for both current polarities, that iscurrent flowing both from left to right and from right to left along thenanowire. Note that for this nanowire 1 volt corresponds to a currentdensity of about 10⁸ A/cm².

Thus, the external magnetic field applied to the domain wall isconfigured to reduce a minimum amplitude of current required of the atleast one current pulse applied to the domain wall to cause thedepinning of the domain wall, to less than a minimum amplitude ofcurrent that would be required of the at least one current pulse tocause the depinning if the external magnetic field were not applied tothe domain wall.

FIG. 22 depicts minimum applied magnetic field required for depinningdomain wall motion with a probability larger than 50%, as a function ofthe number of pulses, for a pulse amplitude of 1.2V, in accordance withembodiments of the present invention. The resonant depinning mechanismdoes not require a large number of pulses. Indeed, large effects arealready observed for only 2 pulses. This is illustrated on FIG. 22,which shows the depinning fields measured for sequences of 1.2V pulsesat resonance, for increasing number of pulses. The resonance is clearlyobserved for a sequence of only 2 pulses, as shown by the significantreduction of the depinning fields.

The scope of the present invention applies generally to depinning adomain wall in magnetic material (e.g., ferromagnetic material) in anytype of magnetic device for any type of pinning potential, through useof electrical current configurations (e.g., a direct current, a currentpulse, a sequence of current pulses, etc.) as described supra. Themagnetic device may comprise any nanostructured magnetic element (e.g.,logic, memory) of any geometric shape (e.g., nanowire, circle, ellipse,prism, column of arbitrary cross-section, U-shaped track as in the shiftregister of FIGS. 1-4, etc.). The pinning potential is due to a spatialdiscontinuity in properties of the magnetic material and consequentlyconfines the domain wall by limiting the spatial extent of the magneticmaterial or by modifying the local magnetic properties of the magneticmaterial such as by doping, irradiation, etc. In one embodiment, themagnetic device is the shift register of FIG. 4 and the associatedpinning potential is due to the alternating magnetic layers therein. Thepinning potential may be provided in a magnetic device formed from ahomogeneous material by shaping the device, including by shaping theboundary of the device (whether an interior or exterior boundary),including the surfaces or edges. The pinning potential may also beprovided in a magnetic device, whether formed from a uniform or anon-uniform magnetic material, by an exterior means. Examples include(a) the passage of current through other nanodevices in the neighborhoodof the first device so as to provide local magnetic fields, (b) thebringing into the proximity of the first device other magnetic materialsso as to use dipole fields from such materials, and (c) the use oflocalized electric fields or voltage potentials to locally (i.e., inlocalized spatial regions) change the magnetic properties of the firstdevice, for example, where the first device if formed from amultiferroic magnetic materials whose magnetic properties (whethermagnetization or magnetic anisotropy or any other magnetic property) canbe affected by electric field. Similarly, the magnetic properties may belocally altered by means of strain for magnetic materials whoseproperties are affected by strain or stress. Similarly, the magneticproperties may be locally altered by temperature. Thus by creating localvariations of the environment, whether magnetic field, electric field,voltage levels, temperature or strain or stress in cases where themagnetic properties of the first device are sensitive to suchenvironmental parameters, a local pinning potential can be provided fromwhich the domain wall may be manipulated using the embodiments describedin this invention.

While experiments have been described with respect to permalloynanowires, magnetic devices may be formed from a wide variety ofmagnetic materials.

While particular embodiments of the present invention have beendescribed herein for purposes of illustration, many modifications andchanges will become apparent to those skilled in the art. Accordingly,the appended claims are intended to encompass all such modifications andchanges as fall within the true spirit and scope of this invention.

1. A method for depinning a domain wall, comprising applying at leastone current pulse to a domain wall that is in spatial confinement by apinning potential to within a local region of a magnetic device, whereineach current pulse has a pulse length sufficiently close to a precessionperiod of the domain wall motion and if the at least one current pulsecomprises at least two current pulses then the current pulses areseparated from each other by a pulse interval sufficiently close to theprecession period such that: the at least one current pulse isconfigured to cause a depinning of the domain wall such that the domainwall moves with sufficient energy to escape the spatial confinement; andeach current pulse has an amplitude less than the minimum amplitude of adirect current that would cause said depinning if the direct currentwere applied to the domain wall instead of the at least one currentpulse.
 2. The method of claim 1, wherein the at least one current pulsecomprises at least two current pulses, and wherein the pulse interval isabout equal to the pulse length.
 3. The method of claim 2, wherein thepulse length and the pulse interval are each about 50% of the precessionperiod.
 4. The method of claim 1, wherein the at least one current pulsecomprises at least two current pulses, and wherein the at least twocurrent pulses are unipolar pulses.
 5. The method of claim 1, whereinthe at least one current pulse comprises at least two current pulses,and wherein the at least two current pulses are bipolar pulses.
 6. Themethod of claim 1, wherein the amplitude of each pulse is less than theminimum direct current by more than a factor of
 2. 7. The method ofclaim 1, further comprising applying an external magnetic field to thedomain wall concurrent with said applying the at least one current pulseto the domain wall, said applied external magnetic field configured toreduce a minimum amplitude of current required of the applied at leastone current pulse to cause said depinning, to less than a minimumamplitude of current that would be required of the at least one currentpulse to cause said depinning if said external magnetic field were notapplied to the domain wall.
 8. The method of claim 1, wherein themagnetic device is a magnetic shift register comprising a track ofalternating domains of ferromagnetic material, wherein the domain wallis between and in direct contact with a first domain and a second domainof the alternating domains, wherein the first domain comprises a firstferromagnetic material, and wherein the second domain comprises a secondferromagnetic material that differs from the first ferromagneticmaterial to create the pinning potential.
 9. A method for depinning adomain wall, comprising: applying at least one current pulse to a domainwall that is in spatial confinement by a pinning potential to within alocal region of a magnetic device, wherein each current pulse has apulse length in a range of 25% to 75% of a precession period of thedomain wall motion and if the at least one current pulse comprises atleast two current pulses then the current pulses are separated from eachother by a pulse interval in the range of 25% to 75% of the precessionperiod, and wherein the applied at least one current pulse is configuredto cause a depinning of the domain wall such that the domain wall moveswith sufficient energy to escape the spatial confinement.
 10. The methodof claim 9, wherein the at least one current pulse comprises at leasttwo current pulses.
 11. The method of claim 10, wherein the pulseinterval is about equal to the pulse length.
 12. The method of claim 11,wherein the pulse length and the pulse interval are each about 50% ofthe precession period.
 13. A structure, comprising a domain wall that isin spatial confinement by a pinning potential to within a local regionof a magnetic device and at least one current pulse applied to thedomain wall, wherein each current pulse has a pulse length sufficientlyclose to a precession period of the domain wall motion and if the atleast one current pulse comprises at least two current pulses then thecurrent pulses are separated from each other by a pulse intervalsufficiently close to the precession period such that: the at least onecurrent pulse is configured to cause a depinning of the domain wall suchthat the domain wall moves with sufficient energy to escape the spatialconfinement; and each current pulse has an amplitude less than theminimum amplitude of a direct current that would cause said depinning ifthe direct current were applied to the domain wall instead of the atleast one current pulse.
 14. The structure of claim 13, wherein the atleast one current pulse comprises at least two current pulses, andwherein the pulse interval is about equal to the pulse length.
 15. Thestructure of claim 14, wherein the pulse length and the pulse intervalare each about 50% of the precession period.
 16. The structure of claim13, wherein the at least one current pulse comprises at least twocurrent pulses, and wherein the at least two current pulses are unipolarpulses.
 17. The structure of claim 13, wherein the at least one currentpulse comprises at least two current pulses, and wherein the at leasttwo current pulses are bipolar pulses.
 18. The structure of claim 13,wherein the amplitude of each pulse is less than the minimum directcurrent by more than a factor of
 2. 19. The structure of claim 13,further comprising an external magnetic field applied to the domainwall, said applied external magnetic field configured to reduce aminimum amplitude of current required of the applied at least onecurrent pulse to cause said depinning, to less than a minimum amplitudeof current that would be required of the at least one current pulse tocause said depinning if said external magnetic field were not applied tothe domain wall.
 20. The structure of claim 13, wherein the magneticdevice is a magnetic shift register comprising a track of alternatingdomains of ferromagnetic material, wherein the domain wall is betweenand in direct contact with a first domain and a second domain of thealternating domains, wherein the first domain comprises a firstferromagnetic material, and wherein the second domain comprises a secondferromagnetic material that differs from the first ferromagneticmaterial to create the pinning potential.
 21. A structure, comprising: adomain wall that is in spatial confinement by a pinning potential towithin a local region of a magnetic device; and at least one currentpulse applied to the domain wall, wherein each current pulse has a pulselength in a range of 25% to 75% of a precession period of the domainwall motion and if the at least one current pulse comprises at least twocurrent pulses then the current pulses are separated from each other bya pulse interval in the range of 25% to 75% of the precession period,and wherein the applied at least one current pulse is configured tocause a depinning of the domain wall such that the domain wall moveswith sufficient energy to escape the spatial confinement.
 22. Thestructure of claim 21, wherein the at least one current pulse comprisesat least two current pulses.
 23. The structure of claim 22, wherein thepulse interval is about equal to the pulse length.
 24. The structure ofclaim 23, wherein the pulse length and the pulse interval are each about50% of the precession period.